Recently, wireless relay networks have become an area of popular research. This is due to their ability to extend communication coverage, increase channel capacity, and improve link reliability. There are two types of relaying strategies: (1) decode-and-forward (DF) relay, whereby a received signal is decoded, re-encoded, and forwarded by a relay device, and (2) amplify-and-forward (AF) relay, whereby a received signal is simply amplified and forwarded to another wireless device or another relay device in the network. The DF scheme is generally used in dedicated relay devices (e.g. relay stations operating in 3GPP LTE-Advanced and IEEE 802.16j systems) which can afford the complexity involved under the DF scheme. However, the AF scheme is generally preferred for battery operated devices as such devices usually have their own data to transmit and the complexity of relaying operation needs to be kept to a minimum (e.g. nodes in smart grid and sensor networks). A disadvantage of the AF scheme is that noise is propagated into or amplified in relayed signals.
The AF relay scheme can be further categorised into fixed gain amplification and variable gain amplification (herein referred to as FAF and VAF respectively). Assuming that the average transmit power at each of the AF relay nodes is 1, the amplification gain for a FAF relay node can be determined by the following formula:
                              α          i                =                              1                                          E                ⁡                                  [                                                                                                          h                        i                                                                                    2                                    ]                                            +                              σ                i                2                                                                        (        1        )            where σi2=E[|ni|2] denotes the noise variance at the i-th relay node.
For a VAF relay node, the amplification gain can be determined by:
                              α          i                =                              1                                                                                                  h                    i                                                                    2                            +                              σ                i                2                                                                        (        2        )            where the instantaneous channel power, |hi|2, at the i-th relay node is used to determine the variable gain.